Department of Engineering and Technology
Signal and Linear System Analysis
Extra Activity
Convolution masks
I hereby declare that I have worked on this homework with academic integrity
Introduction
For this activity we were asked to perform an edge detector filter, show the original
image and the resulting one, the code had to use a convolution and not use the
functions MATLAB has already integrated.
Methodology
First, I investigated different ways to create a mask using matrix and then translate that
in MATLAB language. I ended up finding 3 different methods which presented
similarities between each other.
I started my scrip by assigning the image that the program is going to use, MATLAB
usually makes images a 3 axis matrix (Ex: 3x3x3) so I transformed the image into a 2
dimensional matrix.
The first method is the Sobel Operation Mask, which stablish two matrices of 3x3. One
matrix for the vertical vertex and other for the horizontal vertex (“x” and “y” axis). The
image is passed through a convolution, one for each axis. After both axis have been
passed through the convolution, a variable that adds both axis is assigned and then
output is plotted.
The second method is the Robert’s cross operation Mask. Like Sobel’s method two
matrix are made for each axis, but these matrices have a size of 2x2, this have the
effect of outputting thinner lines when the mask is applied to the image.
The third method is the most efficient method, which is the Laplacian of Gaussian
method. This operation uses just one matrix of 3x3 and just one convolution is needed
to create the mask. The Laplacian of an image with a two-dimensional pixel values can
be given by a second derivate measurement on the image, at the same time this makes
the mask more sensitive to noise than the other methods. As the convolution operation
is associative, I could add a gaussian smoothing filter to obtain a better mask, sadly my
to accomplish this you need an Image processing Toolbox. Nevertheless, the method
still works without the Gaussian filter.
Finally, I plotted the image and the different mask to compared the results.
Script
% David Benavides Banda 371557
% I hereby declare that i have worked on this activity with integrity.
% References:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.301.927&rep=r
ep1&type=pdf
clc
clear
%Images
I=imread('atari.jpg');
I2=I(:,:,1);
%Sobel Operation Mask
GSx=[-1 0 1; -2 0 2; -1 0 1];
GSy=[1 2 1; 0 0 0; -1 -2 -1];
Sx=conv2(I2,GSx,'same');
Sy=conv2(I2,GSy,'same');
Sobel Op
S=abs(Sx)+abs(Sy);
%Sobel Op matrix for Gx and GY
%Convolution of X and Y axis for
%Robert's cross Operation Mask
GRx=[1 0; 0 -1];
and GY
GRy=[0 1; -1 0];
Rx=conv2(I2,GRx,'full');
Ry=conv2(I2,GRy,'full');
Robert's cross
R=abs(Rx)+abs(Ry);
%Robert's cross Op matrix for Gx
%Convolution of X and Y axis for
%Laplacian of Gaussian Mask
MLG=[-1 -1 -1; -1 8 -1; -1 -1 -1];
Iblur1=imgaussfilt(I2,2)
LG=conv2(I2,MLG,'valid');
%Plots
figure('Name','face 1')
subplot(2,2,1)
imshow(I)
title('Original')
subplot(2,2,2)
imshow(S)
title('Sobel Op Mask')
subplot(2,2,3)
imshow(R)
title('Robert´s cross Op Mask')
subplot(2,2,4)
imshow(LG)
title('Laplacian of Gaussian Mask')
Results
As can be seen the different masks worked, and the clearest one is the Laplacian mask,
the Robert’s cross is the second best one. The Sobel Op makes lines thicker which
makes the mask look saturated.
Conclusion
The masks worked correctly, MATLAB have functions which makes more optimized
masks. Nevertheless, the ones made with this procedure work really well. Also, if I had
the image processing toolbox I could program a better mask with the Laplacian of
Gaussian Mask
References:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.301.927&rep=r
ep1&type=pdf
https://la.mathworks.com/help/images/apply-gaussian-smoothing-filtersto-images.html